Difference refinement: obtaining differences between two related structures

There are many examples in macromolecular crystallography where interest focuses on the differences between a previously determined 'native' structure and a nearly isomorphous 'variant'. In such cases, a useful approach to atomic refinement of the variant structure is through weighted least-squares minimization of the residual between the observed and calculated differences in amplitudes of structure factors, a strategy first used in the refinement of deoxycobalt hemoglobin Fermi, Perutz, Dickinson & Chien (1982). J. Mol. Biol. 155, 495-505 and termed 'difference refinement'. For cases in which the modeling errors for the native and variant structures are correlated, theoretical arguments indicate that difference refinement should lead to improved estimates of structural differences when compared with conventional independent refinement. Tests employing simulated peptide data sets and real data from a wild-type protein and a mutant show that difference refinement can substantially reduce errors in the differences between structures when compared with independent refinement. The algorithm is very easy to implement and does not increase the computational demands of refinement.